One often needs to estimate how fast an evolving state of a quantum system can depart from some target state or target subspace of a Hilbert space. Such estimates are known as quantum speed limits. We derive a quantum speed limit for a general time-dependent target subspace. When the target subspace is an instantaneous invariant subspace of a time-dependent Hamiltonian, the obtained quantum speed limit bounds the adiabatic fidelity, which is a figure of merit of quantum adiabaticity. We also compare two states evolving under two different Hamiltonians and derive a bound on the Loschmidt echo.

中文翻译：

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绝热演化、Loschmidt Echo 及其他领域的量子速度极限

人们经常需要估计量子系统的演化状态可以多快地离开希尔伯特空间的某个目标状态或目标子空间。这种估计被称为量子速度限制。我们推导出一般时间相关目标子空间的量子速度限制。当目标子空间是瞬态哈密顿量的瞬时不变子空间时，得到的量子速度极限有界于绝热保真度，这是量子绝热的品质因数。我们还比较了在两个不同的哈密顿量下演化的两个状态，并推导出 Loschmidt 回波的界限。